Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another. One way to test items with ordinal response scales for DIF is likelihood ratio (LR) testing using item response theory (IRT), or IRT-LR-DIF. Despite the various advantages of…

The examination of measurement invariance in polytomous items is complicated by the possibility that the magnitude and sign of lack of invariance may vary across the steps underlying the set of polytomous response options, a concept referred to as differential step functioning (DSF). This article describes three classes of nonparametric DSF effect…

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

Person-fit methods are used to uncover atypical test performance as reflected in the pattern of scores on individual items in a test. Unlike parametric person-fit statistics, nonparametric person-fit statistics do not require fitting a parametric test theory model. This study investigates the effectiveness of generalizations of nonparametric…

U.S. state educational testing programs administer tests to track student progress and hold schools accountable for educational outcomes. Methods from item response theory, especially Rasch models, are usually used to equate different forms of a test. The most popular method for estimating Rasch models yields inconsistent estimates and relies on…

Reviews developments in nonparametric item-response theory (NIRT), from its historic origins in item-response theory (IRT) and scale analysis to new theoretical results for practical test construction. Discusses theoretical results from NIRT often relevant to IRT. Contains 134 references. (SLD)

An automated item selection procedure for selecting unidimensional scales of polytomous items from multidimensional data sets is developed for use in the context of the item response theory model of monotone homogeneity of R. J. Mokken. The procedure is based on the selection procedure proposed by Mokken (1971). (SLD)

This study introduces an order-constrained Bayes inference framework useful for analyzing data containing dichotomous scored item responses, under the assumptions of either the monotone homogeneity model or the double monotonicity model of nonparametric item response theory (NIRT). The framework involves the implementation of Gibbs sampling to…

A method for ordering persons and items when all responses are ordinal was developed and applied to several sets of questionnaire data (from undergraduates) and one set of archeological data. The method provides a possible nonparametric treatment of data usually treated by more traditional psychometric methods. (SLD)

The power of the nonparametric person-fit statistic, U3, is investigated through simulations as a function of item characteristics, test characteristics, person characteristics, and the group to which examinees belong. Results suggest conditions under which relatively short tests can be used for person-fit analysis. (SLD)

Three methods based on the nonparametric item response theory (IRT) of R. J. Mokken for the estimation of the reliability of single dichotomous test items are discussed. Analytical and Monte Carlo studies show that one method, designated "MS," is superior because of smaller bias and smaller sampling variance. (SLD)

The Level-11 vocabulary subtest of the Iowa Tests of Basic Skills was analyzed using a two-stage latent trait approach and data set of 2,356 examinees, approximately 11 years of age. It is concluded that the nonparametric approach leads to efficient estimation of the latent trait. (SLD)

The validity of the assumptions under which the ordinal true score test theory was derived was examined using (1) simulation based on classical test theory; (2) a long empirical test with data from 321 sixth graders; and (3) an extensive simulation with 480 datasets based on the 3-parameter model. (SLD)